Question

Half the perimeter of a rectangular garden whose length is 4m more than it's width is 36m.Find the dimensions of the garden
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Answer 1

Given:

• Half perimeter of garden is 36m.
• Length is 4m more than breadth.

To Find:

• Dimensions of the garden .

Concept Used:

We will use the formula for finding the perimeter of a 'rectangle'.

Solution:

Let us take

• The breadth be x m .
• Length be (x+4)m

Now Formula for finding perimeter of a rectangle :

$\large{\underline{\boxed{\red{\sf{Perimeter_{rectangle}=2(l+b)}}}}}$

where

• l is the length
• b is the breadth.

Using above formula .

$\sf{\implies Perimeter =2(l+b)}$

$\sf{\implies Perimeter =2(x+x+4)}$

$\sf{\implies Perimeter =2(2x+4)}$

$\sf{\implies\dfrac{1}{2}( Perimeter) =\dfrac{1}{2}\times2(2x+4)}$

${\underline{\boxed{\red{\sf{\leadsto \dfrac{1}{2}(Perimeter)=(2x+4)}}}}}$

But its given 36m .

So,

Atq, $\sf{2x+4=36}$

$\sf{\implies 2x =(36-4)}$

$\sf{\implies 2x =32}$

$\sf{\implies x =\dfrac{32}{2}}$

${\underline{\red{\sf{\leadsto x =16m}}}}$

So,

• Length =(x+4)m =(16+4)m =20m
• Breadth =x m =16m